Monk has led Swansea to Premier League safety having been installed as head coach following the sacking of Michael Laudrup in February.
And the 35-year-old looks like being rewarded for the work he has done over the last three months by being given the Swansea job on a long-term basis. It is understood Swansea's board of directors met to discuss the managerial situation yesterday.
And though no official word is likely before next week, it is thought Huw Jenkins and Co believe Monk is the right man to take Swansea forward.
Monk has impressed Swansea's owners having been pitched in at the deep end following Laudrup's exit.
The club's performances under Monk have been largely positive and his team have banked a healthy 15 points from 12 league games under the former skipper.
Monk has made no secret of his desire to remain in charge at the Liberty having coped admirably with the switch from dressing to dugout.
The ex-central defender revealed on Thursday that no discussions had taken place about a contract, but that seems certain to change in the coming days.